Motorised momentum exchange space tethers: the dynamics of asymmetrical tethers, and some recent new applications

MATEC Web of Conferences 148, 01001 (2018) ICoEV 2017 https://doi.org/10.1051/matecconf/201814801001 Motorised momentum exchange space tethers: the dynamics of asymmetrical tethers, and some recent new applications Matthew Cartmell1,2,*, Olga Ganilova1,2, Eoin Lennon1, and Gavin Shuttleworth1 1Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow, G1 1XJ, Scotland, UK 2Strathclyde Space Institute, University of Strathclyde, Glasgow, G1 1XJ, Scotland, UK Abstract. This paper reports on a first attempt to model the dynamics of an asymmetrical motorised momentum exchange tether for spacecraft payload propulsion, and it also provides some interesting summary results for two novel applications for motorised momentum exchange tethers. The asymmetrical tether analysis is very important because it represents the problematic scenario when payload mass unbalance intrudes, due to unexpected payload loss or failure to retrieve. Mass symmetry is highly desirable both dynamically and logistically, but it is shown in this paper that there is still realistic potential for mission rescue should an asymmetry condition arise. Conceptual designs for tethered payload release from LEO and lunar tether delivery and retrieval are also presented as options for future development. 1 Introduction Momentum exchange tether dynamics have been extensively studied in recent years, and are of current considerable interest internationally as a technology for cost effective and environmentally clean propulsion of payload mass from Low Earth Orbit (LEO). A conceptual design for a motorised momentum exchange tether is given in Figure 1 where the central facility motor drive shaft attaches to the propulsion sub-spans by mean of a gantry, mounted so that it can be rotated by the shaft. Typical performance figures for an operational motorised MET on a circular LEO predict an orbit velocity in the region of 7.6 km/s and a tether generated increment of around 3.1 km/s, which has the potential to accelerate the outer payload, at an optimal release position, to around 10.7 km/s. This is fast enough for Earth escape, using a tether made of Spectra2000TM. It should be noted that a fundamental requirement for motorised spin is shown in Figure 1 comprising a counter-inertia in the form of an additional pair of tethers and counter-masses attached to the motor stator [1]. This sub-system is required to satisfy Newton’s third law of motion and is not analysed here but is assumed to be present, coupling through the drive motor electrodynamics in order to provide the requisite operational configuration. Fig. 1. A motorised momentum exchange tether in LEO. A fairly comprehensive review of space tether research up to 2008 is given in [2] and a detailed study of fundamental rigid-body motorised tether system dynamics is given in [3, 4]. Tether flexure, accommodating various forms of vibration, is discussed in full in [5]. Important mission scenarios for motorised tethers are discussed in [6, 7]. The fundamental issue with asymmetrical payload mass distribution is that the centre of mass location of the tether will then change on orbit, introducing dynamic perturbations that will de-orbit the tether, with potentially disastrous consequences for the mission. In order to maintain the orbit, and also to capitalise on opportunities offered by the exploitation of orbital harmonics, payload mass symmetry is required. In terms of mission architecture this allows a simultaneous in and out flow of payload from the location of the host planet to the destination planet [6]. On the basis that symmetry (defined as the tether being laden with two payloads of identical mass properties *Corresponding author : © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). MATEC Web of Conferences 148, 01001 (2018) ICoEV 2017 https://doi.org/10.1051/matecconf/201814801001 Y located at both ends, or, conversely, no payloads on either end of the tether) cannot be absolutely guaranteed, a study of the asymmetrical mass distribution problem was seen to be necessary. In this paper an initial model is proposed, with some calculations that suggest that a pragmatic level of reserve chemical propulsion on board each payload could be used to rescue a mission in which asymmetry has arisen for some reason. This is investigated in the form of the complete loss of one of the payloads. This is followed by discussions of two further investigations in which the tethered release of small payloads from an Earth orbiter and the use of a specialised lunavator tether with an end reeling facility for lunar touchdown are investigated. These two application scenarios in fact reflect different levels of mass symmetry requirement and on that basis they provide interesting platforms for further research into robust solutions to the tether asymmetry problem. Mp ⚫ y0 12 𝑛𝑛 𝑈𝑈 = − ∑ 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 (2𝑗𝑗 − 1)2 𝑙𝑙 2 (2𝑗𝑗 − 1)𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑗𝑗=1 𝑛𝑛√ − + 𝑅𝑅2 𝑛𝑛 4𝑛𝑛2 𝑛𝑛 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 − ∑ 2 2 (2𝑗𝑗 − 1)𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 (2𝑗𝑗 − 1) 𝑙𝑙 2 𝑗𝑗=1 𝑛𝑛√ + + 𝑅𝑅 𝑛𝑛 4𝑛𝑛2 𝜇𝜇𝑀𝑀𝑝𝑝 − √𝑙𝑙 2 − 2𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝑅𝑅2 𝜇𝜇𝑀𝑀𝑝𝑝 𝜇𝜇𝑀𝑀𝑚𝑚 − 𝑅𝑅 √𝑙𝑙 2 + 2𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝑅𝑅2 x0 l ⚫ Mp R(t θ E X Fig. 2. A planar dumb-bell tether in LEO where E represents the centre of the Earth and EXY is an Earth fixed frame. Lagrange’s equations are used to obtain three differential equations of motion based on generalised coordinates R(t), θ(t), and ψ(t). These are intricately coupled, nonlinear, and lengthy, and are not reproduced here but are obtainable in full in [3]. They represent the planar orbital dynamics of the tether, accommodating orbital eccentricity. The data used for the study is as follows. Tether sub-span length l = 50 km, payload masses Mp = 1000 kg, central facility mass Mm = 5000 kg, tether density ρ = 970 kg/m3, crosssectional area A = 62.83*10-6 m2, equal radii of central facility and payloads rm = rp = 0.5m, standard gravitational parameter μ = 3.9877848*1014 m3/s2, drive torque τ = 5MNm, and integration time = 86400 s. Initial conditions are R(0) = 6870000 m, θ(0) = 97.1877 rad, and ψ(0) = 0 rad, and R’(0) = 0 m/s, θ’(0) = 0.00121485 rad/s, and ψ’(0) = 0 rad/s. These initial conditions accommodate an elliptical LEO (e = 0.20004) on which the tether’s long-term motion is predicted to be in the form of a monotonic spin. The tangential velocity of the payloads relative to the COM at the centre of the system builds up usefully. We note that the centripetal stress is proportional to the angular velocity squared. The system responses in the time domain are given in the following Figures. Figure 3 shows a continuous build-up in the angular position of the tether over time, with Figures 4 and 5 indicating the increasing angular velocity and the tangential velocity of the tip of each sub-span relative to the spin axis located at the CoM of the (...truncated)